## 01 November 2015

### It's not time to blow up the New Keynesian model

Scott Sumner wrote a blog post recently in which he questioned the validity of New Keynesian models. He listed five of it's predictions that he finds troublesome:

1. The NK model implies that higher taxes on wages can be expansionary.
2. The NK model implies that higher capital gains taxes can be expansionary.
3. The NK model implies that raising the aggregate wage level by government fiat can be expansionary.
4. The NK model implies that an increase in the fed funds target can be expansionary.
5. The NK model implies that an fiscal austerity can be expansionary, if done by slowing the growth in government spending
His first three claims are hardly criticisms applicable to New Keynesian theory in general, but they do accurately point out that New Keynesian models turn a bit wonky at the zero lower bound. It is the last two claims that are particularly nefarious.

The fourth claim is ignorant of the fact that Neo-Fisherian results are entirely dependent on the existence of multiple equilibrium which arise from ambiguous fiscal policy and the absence of monetary policy rules. Inflation should really be considered indeterminate during an interest rate peg (as it was until the Neo-Fisherians decided to implicitly assume active fiscal policy). Alternatively, a theory of money demand could be added to New Keynesian theory that could solve the problem than discretionary interest rate control policy creates.

Sumner refers to Nick Rowe's recent (and quite good) post on New Keynesian fiscal policy as evidence for his fifth attack on New Keynesian models. What he doesn't realize, though, is that what Nick Rowe describes in his post is not consistent with higher output. Actually, the government is causing potential output to change by moving government spending around. Lower government spending is consistent with lower potential output. To understand why, it is necessary to look at Real Business Cycle theory. In RBC models, permanent changes in government spending have real (supply side) effects that change output. These supply side effects are present in New Keynesian models, and in this case they move potential output around which, in turn moves the natural rate of interest around. Expected austerity does raise the natural rate of interest, but it does not actually raise output.

Contrasting his own views with those he associates with New Keynesian models, Sumner provides four characteristics of the "musical chairs model":
1. In the short run, employment fluctuations are driven by variations in the NGDP/Wage ratio.
2. Monetary policy drives NGDP, [sic] by influencing the supply and demand for base money.
3. Nominal wages are stick in the short run, and hence NGDP shocks cause variations in employment in the same direction.
4. In the long run, wages are flexible and adjust to changes in NGDP. Unemployment returns to the natural rate (currently about 5% in the US.)
As I noted in my comment, this set of four characteristics is not a model. It can be made into a model perhaps, but it falls short of actually being a model. If someone were to write down the "musical chairs model" as Sumner describes it, it would likely closely resemble a New Keynesian model where the primary friction is changed from sticky prices to rigid nominal wages and the central bank uses the monetary base, rather than the nominal interest rate, as the instrument for monetary policy.

Naturally, this leaves Sumner with the task of coming up with a money demand function that is both empirically accurate and gets around the problems that I wrote about here and here so that he doesn't have to drop his assertion that monetary expansion, even at the zero lower bound, is always expansionary, rather than useless as most plausible models of money demand (and the empirical evidence) seem to suggest. I suggest Sumner add his money demand function to this model by Stephanie Schmitt-Grohe and Martín Uribe and see if it performs as well as New Keynesian models when put to the data.

1. I think there is tension between your admonishment that Sumner should provide a money demand function that supports the idea that monetary expansion is always expansionary, versus the reality of actual monetary policy, which is that the real effect of fiddling with monetary policy instruments (OMO, IOR etc) is inextricably tied to market expectations of what the Fed might do next. Nick Rowe has a great post making this point here:

In the market monetarist view, "monetary expansion" does not simply printing dollars and swapping them for treasuries. "Monetary expansion" means doing something that raises the market expectation of future NGDP. I don't know how to capture that idea in equations, but given that definition, it is almost obvious that monetary expansion is expansionary even at the ZLB.

I am not here to defend Scott's comments about the NK model, about which I know very little. But I do believe that Scott has a fundamentally better approach to monetary policy than we practice today, and it really matters. The Fed should target stable aggregate demand, and should tell the market that that's what it's going to do, and look to the market to see if it's on track to succeeding. It would make the world a better place. Even if Scott's fourth point about NK models isn't quite right somehow.

Kenneth Duda
Menlo Park, CA

2. Thanks for commenting!

I do really think Sumner (and Market Monetarists in general) need to provide good reasons for why they think monetary expansion at the zero lower bound works besides just stating that they assume it does or that it works because agents expect it to. As far as I know, agents in Market Monetarist models must be irrational or Market Monetarists just have terrible microfoundations for their money demand functions.

"In the market monetarist view, "monetary expansion" does not simply printing dollars and swapping them for treasuries. "Monetary expansion" means doing something that raises the market expectation of future NGDP."

That, to me, reads "the market monetarist definition of monetary expansion is monetary expansion that works at the zero lower bound." That's like saying the increase in the monetary base since 2008 was not effective, so it doesn't count as a monetary expansion.

Perhaps and NGDPLT is the right way to go, but I think Sumner and other Market Monetarists should focus more on explaining why they think NGDPLT is good (like Nick Rowe does) than asserting that central banks can do whatever they want regardless of the circumstances.

Thanks again for commenting.

3. John. thanks for the response.

Your input about what market monetarists should do to effectively advance the cause are very important to me. I have invested significant time and money in pushing for better monetary policy in this country, and I want to learn how to be more effective. It sounds like you want a model ... a microfounded money demand function? I don't really get what would be convincing to you. Could you help me figure that out? You say you want market monetarists to be "more like Nick Rowe" (isn't he a market monetarist?) by "focusing more on explaining why NGDPLT is good". Sumner has done some of that, e.g.

http://www.nationalaffairs.com/publications/detail/re-targeting-the-fed
http://mercatus.org/publication/market-driven-nominal-gdp-targeting-regime
http://www.nationalreview.com/articles/255093/money-rules-scott-sumner/page/0/1

but maybe he has not been convincing. What would a convincing argument supporting NGDPLT look like?

(I'll give you the argument I find convincing in my next comment, because I went over the 4k limit :-)

4. Yow, looks like dollar-signs go into math mode? $\int_0^x e^xdx$ ?

5. In objecting to the "assertion that central banks can do whatever they want", it sounds like you are saying you think it is impossible for the CB to raise NGDP expectations when at the ZLB. Well, it sure looks that way doesn't it --- no matter what the Fed does with QE, the market inflation forecast (interest rate forwards, TIPS spreads, whatever) keep telling the Fed the parrot is dead. So the Fed is powerless. Right?

No, not at all. Things are broken because the Fed is doing it all wrong. It tells the market, "we are caring people, so we are kind of concerned about unemployment, and a bit worried about deflation, etc. So we're going to mess around with zero interest rates, QE, etc. But mark my words: we fought hard in the 1980's to win credibility and establish a nominal anchor. We will never, ever sacrifice that. You want to see 4T of bank reserves disappear in a heartbeat? Just you try pushing PCE inflation about 2% and see what happens to you. Just try it! We dare you!" And it turns out the markets are smart enough to not bet against the Fed. The market says, "yeah. Gotcha." And that's that. The newly created money just sits. The Fed prints it, buys bonds, and then borrows it all right back again as excess reserves. It's ridiculous.

So, here's an example of doing it right. The Fed would say:

1. We are done with worrying about inflation. We have no inflation target. You guys in the market figure out what the price level should be.

2. We don't care about interest rates either. Markets can figure that out.

3. Unemployment? Same thing. Employers will figure out how many people to hire. Aren't markets great?

There! Now that all three aspects of our "dual mandate" are out of the way, we can move on to what we do care about. It's only one thing: ....... um,... NGDP... or total nominal labor compensation.... or ... look, it doesn't really matter, pick a nominal aggregate, it is fine tuning to worry about which one. So okay, let's pick NGDP. We intend to drive the level of NGDP to 5% higher than today over the next 12 months. And the year after that, 10.25% higher than today, and the year after that, 15.7625% higher than today. (Our target goes up 5% a year regardless of what actual NGDP does).

Now, the market is telling us we aren't going to hit that. (Maybe they're still laughing at us for undershooting our inflation target 27 quarters in a row.) But this time is different, and we'll prove it. Until the market forecast rises to our target, we will lower IOR by 25 basis points every month. That's right, in a year we'll be at -0.75% IOR. Let's see what the banks do with 4T of negative-interest-bearing reserves. Also, we are going to buy 100B worth of treasures this month, double that next month, and keep doubling until we own them all. And we've decided to collect yen and euros as well, 100B this month, 200B next month, let's see, can we buy them all? Probably not, because the ECB can print as any as it likes, but let's find out if they will. Did I mention gold? We're buying 100B a month of that too. We will keep buying every asset we're allowed to buy, doubling the amount we buy each month, until we either own the entire world, or the market tells us we'll hit our NGDP forecast.

As the market monetarists say, the Fed is master of the nominal universe. Constraints are all either political or imagined.

-Ken

6. Sorry for the turds I left on this comment thread... I lost the battle with Blogspot on the meaning of a dollar-sign.

7. Yeah, dollar signs activate mathjax (https://www.mathjax.org/).

I like to think of Nick Rowe as a model for his fellow Market Monetarists. He doesn't spew "NGDP" as profusely as others and spends a lot of time distilling complicated economic theory into something that is easily understandable.

Scott has made some good arguments for NGDP targeting. For a time, I actually considered an NGDPLT optimal, but I realized that that conclusion hinges on the frictions present in an economy. Nominal wage rigidity is one friction that makes an NGDPLT seem better than an inflation target or a price level target.

Good money demand functions are something that the whole field of macroeconomics has been deficient in for a while. The theory that does exist (i.e. Cash-in-Advance and Money-in-the-Utility function) is either pretty simplistic or reliant on bad assumptions. Market Monetarists are subject to my criticism in this area mostly because they think monetary policy is effective at the zero lower bound and I don't think they've given a good explanation as to why they think this is the case, especially in a formal model.

I hope this helps.

8. Thanks, John. I'm confused by your comment about money demand functions. The "cash-in-advance" money demand function doesn't seem to correspond to our reality at all. Clearly, there is a ton more money in the banking system now than is required to satisfy some cash-in-advance constraint that our economy doesn't actually have in the first place because of, you know, credit. As for "money in the utility function"... I couldn't find a wikipedia page for this one, but I presume this is some model where people like to hold money because it makes them happy, which seems like a non-promising foundation for monetary policy. Explaining why people want to hold 5 times as much money in 2010 than 2007 will take some ... explaining. Sort of like the RBC people who blame the unemployment of 2010 on a sudden shift in preference for leisure over work among the desperately poor, a notion that strains credibility to put it politely.

More broadly, I'm not seeing how fiddling with money demand functions would help me push for better monetary policy. If I could somehow come up with some money demand function that was at least consistent with the last 20 years, I'm not seeing how that would help anything. I have no reason to think the money demand function will look like that in the future. Market monetarism does not depend on any particular money demand function; it relies on the market to tell the Fed what money demand will be like, so the Fed can adjust the supply accordingly.

I'm surprised you had no reaction to my argument that the CB has plenty of power at the ZLB, if it chooses to use it. I see you have other posts claiming that the CB cannot get traction there. Krugman is more careful, always emphasizing that it's *conventional* monetary policy that dies at the ZLB (which is of course true if you define "conventional monetary policy" as interest rate targeting.)

I ask you to think about how you could set your intellect to work at pushing for better monetary policy, and let me know (kjd@duda.org) if you have ideas. I stand by ready to fund credible efforts to improve things.

Thanks,
-Ken

P.S. I don't think NGDPLT is optimal, just that it's much better than current policy at dealing with a low natural rate of interest, and because of that alone, we should support it, for the sake of millions of needlessly unemployed people.

9. "The "cash-in-advance" money demand function doesn't seem to correspond to our reality at all. Clearly, there is a ton more money in the banking system now than is required to satisfy some cash-in-advance constraint that our economy doesn't actually have in the first place because of, you know, credit."

I completely agree, cash-in-advance is not a good model of money demand (cash-credit models, like the one I wrote about here (http://ramblingsofanamateureconomist.blogspot.com/2015/09/a-detailed-derivation-of-my-favorite.html) have a little bit of promise).

"As for 'money in the utility function'... I presume this is some model where people like to hold money because it makes them happy, which seems like a non-promising foundation for monetary policy."

I also completely agree with you here. MIUF is a stupid assumption. Both CIA and MIUF models point to the fact that money demand is an underdeveloped part of macroeconomics in general and still seems to be largely ignored, except perhaps by new monetarists (e.g., Stephen Williamson and David Andolfatto), whose models I haven't looked too deeply into yet (there's something about how they explain their models in the same needlessly confusing way that Robert Lucas does that makes their papers hard for me to read).

The main reason I'm interested in having Market Monetarists come up with a money demand function is that I don't think the current models are congruent with the Market Monetarist claim that monetary policy works at the zero lower bound. Perhaps I need to reread Krugman's 1998 paper and see what the reasoning for the idea that monetary expansions that are expected to be permanent working even at the zero lower bound is.

Personally, I think Taylor Rules are the wrong way to conduct economic policy because they exhibit multiple equilibria (one equilibrium has inflation on target, the other is at the zero lower bound with deflation at the rate of time preference). My current position is that the Fed should have a Taylor-type rule for monetary base growth. If money demand in the real world is truly too unstable, then this would be a bad policy, but the evidence seems to suggest that money demand is roughly a decreasing function of the opportunity cost of holding money and an increasing function of real GDP. When the opportunity cost of money is sufficiently low, it appears that demand for money becomes indeterminate so monetary expansions have no set impact on the economy.

1. Jose Romeu Robazzi05 November, 2015 04:31

Hello, Mr. Handley, this is the first time I read your blog, I am impressed with the quality of the posts, congratulations. I have been following this discussion with high interest, since I read your comments on a Scott Sumner post. I too am intrigued by the task of modeling the money demand function. But as a financial markets practitioner, I know for a fact that with regard to money, people can believe almost anything. In general terms, it looks to me that the assertion that at the ZLB, money demand "becomes indetermined" is a fair conclusion (empirically). But not helpful. Theoretically, it is possible that a monetary authority can buy all assets in an economy, and at some point, nominal spending grows. The fact that we have not seem it happening is not an indicative that it is impossible. Seven years ago, the US base money aggregate was something like 800 billion dollars, and if you said that it would be multiplied by 5 in the next couple of years, anybody could say there would be lots of price inflation associated with it. A lot of people did that, and I lot of peple were wrong. That is because money demand increased even more. Now, it does not mean that if we had multiplied base money 10 times, the result would be the same, because money demand is "indetermined". The fact that we never reached a "saturation point" in money printing does not mean it doesn't exist. Nobody has ever seen an electron, but the fact that we have electricity shows we can believe it exists based on other phenomena. That is why I like the NGDP idea. NGDP is for the money demand function what electricity is for an electron (something that nobody has ever seen). Sorry for the physiscs analogy, but I am an engineer, and that was the first thing that came to my mind... I would be interested in hearing your thought on my comment. Thank you.

2. Jose,

I'm glad you like my posts so far.

"In general terms, it looks to me that the assertion that at the ZLB, money demand "becomes indetermined" is a fair conclusion (empirically). But not helpful. Theoretically, it is possible that a monetary authority can buy all assets in an economy, and at some point, nominal spending grows."

I disagree that the result of this model is "not helpful" (also, I am not asserting that money demand is indeterminate at the zero lower bound, I am deriving it from the assumption of a cash-in-advance constraint and the assumption of utility maximization). I think it's very helpful to know that, in common theoretical specifications of money demand, real money demand (and therefore the price level) is indeterminate at the zero lower bound. From that we can conclude that empirically we should not observe monetary policy being effective at the zero lower bound.

"Now, it does not mean that if we had multiplied base money 10 times, the result would be the same, because money demand is "indetermined"."

The model above says that it does mean that if we multuplied the monetary base by ten instead of five, money demand would still be indeterminate and the price level would still be indeterminate.

Scott Sumner seems to have the problem of confusing assertion and result derived from assumption too. He's written a post asking someone to come up with a model that gives the results he wants, not that has the assumptions he wants. Good economics (and science) doesn't occur when we begin with a conclusion and then build a model to support it. Instead, we should start with assumptions about preferences, expectation formation, and types of nominal rigidity and then derive the policy conclusions that those assumptions bring.

Thanks for commenting,

John

3. Jose Romeu Robazzi06 November, 2015 03:32

Hello, John, thanks for paying attention to what I have to say. Moving on, we don't know what would have happened if we raised the monetary base by 10 x instead of 5x. That is what I tried to say. The fact that a certain model predicts indeterminacy and the data failed to reject that indeterminacy it does not mean the model is correct. Let's take another model, one very simple, a marginalist model, where the hypothesis is that a very abundant thing (i.e. money) may command a lower price (in terms of goods). Let's also assume we don't know the closed form relationship between money price and money quantity. One way to "test" this theory is to increase the quantity of money until the price of money falls. The fact that we have increased the quantity of money and money prices have not fallen may be explained by an increase in the demand for money in a relationship we don't know, But it could a be nonlinear, non differentiable relationship that has an inflection point at higher quantities, let's call that quantity a "saturation point". You might say, that is a model that "fits the conclusion you want to reach". But against that I would say: we have seen hyperinflation, and historically, in many countries and with many institutional setups, that observable fact has been linked to money growth. So, why is it so incredible that any monetary authority can produce a decrease in the price of money by just increasing money quantity enough? I think that the empirical evidence suggests this is possible. The fact that we have not reached the "saturation point" does not mean it does not exist, it just means we don't know how high it is.

4. Jose,

When I was writing my previous comment, I didn't realize that it was on this post instead of the next one. When I mentioned "the model above" I was talking about the model in this post: http://ramblingsofanamateureconomist.blogspot.com/2015/11/monetary-policy-effectiveness-in.html

I make a couple of references to that model in the comment below, but I'm pretty sure I explain my reasoning well enough independently of the post.

"we don't know what would have happened if we raised the monetary base by 10 x instead of 5x."

No, we don't know. Just because we don't know doesn't mean we can't guess. Or, better yet, we could collect a set of facts and assumptions, make a model, and see what it says. That's called science. I agree that the fact that the data corroborated the model twice (Great Depression and Great Recession) does not prove that, 100% of the time, monetary expansion at the zero lower bound will be useless. The only way I see that practically changing is if cash is eliminated so that the central bank can make sure that money never dominates safe assets in the interest it pays.

"The fact that we have increased the quantity of money and money prices have not fallen may be explained by an increase in the demand for money in a relationship we don't know"

Sure. I guess you could resign yourself to not trying to figure out why demand for money increased. The evidence seems pretty clear why to me, though. Generally you would expect demand for something to increase if the cost of holding it decreased. At the zero lower bound, the cost of holding money instead of other assets is effectively zero, so you should expect the demand for money to be indeterminate. What happens to the demand for a good when the price is zero?

"I would say: we have seen hyperinflation, and historically, in many countries and with many institutional setups, that observable fact has been linked to money growth."

Nothing about the model I wrote about in the post suggests a hyperinflation can not happen. Normally, the central bank has absolute control of the rate of inflation in Cash-In-Advance models, so hyperinflations are do to high money growth. It just so happens that these models predict that money growth is irrelevant at the zero lower bound. Are you aware of any hyperinflations that have occurred at the zero lower bound? I certainly haven't heard of any.

10. Thanks for the response, John. I'm feeling in sync. Thanks for translating the econ ideas to English for me.

Your idea of a "Taylor-type rule for monetary base growth" corresponds well to the first step towards NGDPLT, which is to aim for your final target (whatever it is) by setting the monetary base size directly, rather than setting an interest rate target. (Interest rate targets are awful because they fall apart at the ZLB.)

I'm curious what your Taylor-type rule would target. The problem with targeting inflation is how do you work the employment side of the dual mandate in? Would you try to combine inflation and unemployment into one metric to target? If you did that, and picked NGDP as that unified target, you'd be another step towards NGDPLT.

The next step is to recognize the need to target the *level* of NGDP, not its growth rate, to force expectations along the right path... and the final step is to recognize that you have no idea what the size of the monetary base should be to hit your NGDP level target, so you should outsource the exercise of deciding to the market.

Thanks,
-Ken

1. ”I'm curious what your Taylor-type rule would target. The problem with targeting inflation is how do you work the employment side of the dual mandate in? Would you try to combine inflation and unemployment into one metric to target? If you did that, and picked NGDP as that unified target, you'd be another step towards NGDPLT.”

In models where the only friction is sticky prices, targeting inflation by itself is enough to ensure full employment most of the time. Of course, other frictions, such as nominal wage rigidity make it so that strict inflation targeting is a less optimal policy. This is why the Taylor Rule also reacts to the output gap (or the unemployment rate); central banks seem to acknowledge that basic New Keynesian DSGE's do not account for all the frictions in the economy. In some ways, an NGDPLT isn't far off from a price level target combined with some response to the output gap. An argument that proponents of NGDPLT could be making is that central banks need to pay equally as much attention to gaps in the price level from trend as gaps in output from trend. I personally don't see why the output gap should be weighted very heavily, especially if sticky prices are the primary friction in the economy.

Maybe different countries should target different things depending on the severity of the frictions in each country. Countries with a lot of wage rigidity would target NGDP or some aggregate wage index while countries with a lot of price rigidity would target inflation or the price level.

"the final step is to recognize that you have no idea what the size of the monetary base should be to hit your NGDP level target, so you should outsource the exercise of deciding to the market."

This is why New Keynesian economics has been so focused on Taylor Rules. It's pretty much universally agreed upon that rules beat discretion in terms of monetary policy (I wish the same was true for fiscal policy) because central banks don't seem to magically know what interest rate, or equivalently what size of the monetary base, is consistent with them achieving their target.

11. Now I'm just confused. What do you think we should actually do?

Regardless of what the models say, inflation targeting does not work well in practice. For example, in the US, shelter inflation has been outstripping non-shelter inflation for years, and that's because of a supply constraint (our refusal to build in our most productive regions, e.g. SF Bay Area), not because of excessive AD. If the central bank insists on a 2% inflation target, and shelter inflation runs at 4% in dense metro areas because of local supply constraints, we are in for a very painful ride. Why would you inflict that on millions of people who don't live anywhere near?

An NGDP target would not have this problem. The Fed would ensure that nominal spending is stabilized so people outside of the SF Bay Area get to keep their jobs. If shelter inflation goes even higher, so be it. The bay area should liberalize its construction policies, there's nothing the Fed can do. A nationwide AD shortfall is not a good solution to rising rents in Mountain View.

See http://idiosyncraticwhisk.blogspot.com/2015/08/july-2015-inflation-and-our-very-low.html for more on how shelter inflation in certain geographies is leading the Fed to overly tight monetary policy.

I think "rules beat discretion" is a fine mantra, but the idea that something as simple as a Taylor rule could work well in all future economic conditions strikes me as naive, and if you argue you'll just change the rule when it no longer fits, then what does it even mean to have a rule? NGDPLT (or any nominal aggregate level targeting) does not have this problem because the hard part is outsourced to the markets, which can completely change their paradigm any time they want without introducing central bank discretion.

-Ken

1. Ken,

"Regardless of what the models say, inflation targeting does not work well in practice. For example, in the US, shelter inflation has been outstripping non-shelter inflation for years, and that's because of a supply constraint (our refusal to build in our most productive regions, e.g. SF Bay Area), not because of excessive AD. If the central bank insists on a 2% inflation target, and shelter inflation runs at 4% in dense metro areas because of local supply constraints, we are in for a very painful ride. Why would you inflict that on millions of people who don't live anywhere near?"

The fact that the relative price of shelter has been increasing is not the fault of inflation targeting. Relative prices generally increase for supply side reasons, the trend rate of inflation does not matter for the relative price of shelter. If trend inflation was 4%, shelter inflation would probably be 6%.

"I think "rules beat discretion" is a fine mantra, but the idea that something as simple as a Taylor rule could work well in all future economic conditions strikes me as naive, and if you argue you'll just change the rule when it no longer fits, then what does it even mean to have a rule?"

I don't think that we should change monetary policy rules very often. That's partly why I don't think the Federal Reserve should drop its 2% inflation target so quickly (the Fed has only been explicitly targeting 2% PCE inflation for a short period of time). The Fed should commit to a rule and stick to it so that expectations can be anchored.

Also, the only time I would see changes in the nominal aggregate that is targeted as necessary is when the underlying frictions in the economy change so much that the old target is inefficient. If the poor recovery from the Great Recession really is a result of downward nominal wage rigidity, then perhaps we do need a higher inflation target or to target NGDP or an aggregate wage index. Or, if the poor recovery has been because of financial frictions, maybe the Fed needs to target financial stability.